BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

rate problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 79
Joined: Mon Feb 13, 2012 3:02 pm
Thanked: 2 times
Followed by:3 members

rate problem

by jzw » Mon Feb 13, 2012 3:07 pm
I'm usually good with rate problems, this one has got me confused. How do I set this up? I'm comfortable with the pie method or the chart method. Thanks in advance for the help.

Caroline's and Carl's Cupcakes receive an order for a certain number of cupcakes. Caroline takes eight hours to complete a fraction of the order while Caroline's partner, Carl, takes sixteen hours to complete the rest of the order. How many hours would it take for Caroline to complete the order alone if Caroline made four times as many cupcakes in eight hours as Carl made in sixteen hours?
Top
Source: — Problem Solving |
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pm
Thanked: 158 times
Followed by:21 members

by pemdas » Mon Feb 13, 2012 3:31 pm
jzw wrote:I'm usually good with rate problems, this one has got me confused. How do I set this up? I'm comfortable with the pie method or the chart method. Thanks in advance for the help.

Caroline's and Carl's Cupcakes receive an order for a certain number of cupcakes. Caroline takes eight hours to complete a fraction of the order while Caroline's partner, Carl, takes sixteen hours to complete the rest of the order. How many hours would it take for Caroline to complete the order alone if Caroline made four times as many cupcakes in eight hours as Carl made in sixteen hours?
There are two fractions of order completed by Caroline and Carl, let's denote them A and B, they sum up to the total of one (1) complete order for a certain number of cupcakes, A+B=1.
Their speeds are A/8 Caroline's and B/16 Carl's. The relationship between A and B is further given as 8*(A/8)=4*16(B/16) or A=4B. To find time, within which Caroline completes the order alone, we need to define the fraction of work completed by her.

A=4B
A+B=1

5B=1 and B=1/5, hence A=4/5. The fraction of work completed by Caroline is 4/5.

If 4/5th fraction of work takes Caroline 8 hours, then
1 (one, i.e. complete) work will take her t hours

find t?
t=8:4/5=10 hours

answer 10 hours
Success doesn't come overnight!
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Mon Feb 13, 2012 6:17 pm
jzw wrote:I'm usually good with rate problems, this one has got me confused. How do I set this up? I'm comfortable with the pie method or the chart method. Thanks in advance for the help.

Caroline's and Carl's Cupcakes receive an order for a certain number of cupcakes. Caroline takes eight hours to complete a fraction of the order while Caroline's partner, Carl, takes sixteen hours to complete the rest of the order. How many hours would it take for Caroline to complete the order alone if Caroline made four times as many cupcakes in eight hours as Carl made in sixteen hours?
Let Carl's rate = 2 cupcakes in 16 hours.
Since Caroline produces 4 times the number of cupcakes in 8 hours, Caroline's rate = 8 cupcakes in 8 hours = 1 cupcake per hour.
Total number of cupcakes = cupcakes produced by Caroline in 8 hours + cupcakes produced by Carl in 16 hours = 8+2 = 10.
Time for Caroline alone to produce 10 cupcakes = w/r = 10/1 = 10 hours.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Senior | Next Rank: 100 Posts
Posts: 32
Joined: Mon Oct 31, 2011 4:41 am
Thanked: 2 times

by LeoBen » Tue Feb 14, 2012 3:44 pm
GMATGuruNY wrote:
jzw wrote:I'm usually good with rate problems, this one has got me confused. How do I set this up? I'm comfortable with the pie method or the chart method. Thanks in advance for the help.

Caroline's and Carl's Cupcakes receive an order for a certain number of cupcakes. Caroline takes eight hours to complete a fraction of the order while Caroline's partner, Carl, takes sixteen hours to complete the rest of the order. How many hours would it take for Caroline to complete the order alone if Caroline made four times as many cupcakes in eight hours as Carl made in sixteen hours?
Let Carl's rate = 2 cupcakes in 16 hours.
Since Caroline produces 4 times the number of cupcakes in 8 hours, Caroline's rate = 8 cupcakes in 8 hours = 1 cupcake per hour.
Total number of cupcakes = cupcakes produced by Caroline in 8 hours + cupcakes produced by Carl in 16 hours = 8+2 = 10.
Time for Caroline alone to produce 10 cupcakes = w/r = 10/1 = 10 hours.
Hi Mitch,

Would you be able to help me here? I normally would solve the work-based problems using the method you have given here -- i.e. plugging in.

However, I tried to do this using rtw or chart method. and i get a different answer, not sure. pls can check if this is correct?

assuming carolina is A and her partner is B, lets say B's rate is x, and its given that A's rate 4 times B's ==> A's rate = 4x; thus the below table

------- A ------- B
R------ 4x ------ x
T------ 8 ------- 16
W------ 32x------ 16x

it follows that total work done is 48x. now is A is to do the entire work alone then let t be the time. rt = w; 4xt = 48x ==> t = 12.

what is wrong here, pls help. thanks.
Top
Senior | Next Rank: 100 Posts
Posts: 32
Joined: Mon Oct 31, 2011 4:41 am
Thanked: 2 times

by LeoBen » Tue Feb 14, 2012 4:13 pm
Sorry to bother. I just realised my imbecility. :( Instead of work, i was trying match up the 4 times to rate. Corrected in the below now. :)
LeoBen wrote:
GMATGuruNY wrote:
jzw wrote:I'm usually good with rate problems, this one has got me confused. How do I set this up? I'm comfortable with the pie method or the chart method. Thanks in advance for the help.

Caroline's and Carl's Cupcakes receive an order for a certain number of cupcakes. Caroline takes eight hours to complete a fraction of the order while Caroline's partner, Carl, takes sixteen hours to complete the rest of the order. How many hours would it take for Caroline to complete the order alone if Caroline made four times as many cupcakes in eight hours as Carl made in sixteen hours?
Let Carl's rate = 2 cupcakes in 16 hours.
Since Caroline produces 4 times the number of cupcakes in 8 hours, Caroline's rate = 8 cupcakes in 8 hours = 1 cupcake per hour.
Total number of cupcakes = cupcakes produced by Caroline in 8 hours + cupcakes produced by Carl in 16 hours = 8+2 = 10.
Time for Caroline alone to produce 10 cupcakes = w/r = 10/1 = 10 hours.
Hi Mitch,

Would you be able to help me here? I normally would solve the work-based problems using the method you have given here -- i.e. plugging in.

However, I tried to do this using rtw or chart method. and i get a different answer, not sure. pls can check if this is correct?

assuming carolina is A and her partner is B, lets say B's produce or work done is x, and its given that A's produce is 4 times B's ==> A's work = 4x; thus the below table

------- A ------- B
R------ x/2 ------ x/16
T------ 8 ------- 16
W------ 4x------- x

it follows that total work done is 5x. now as A is to do the entire work alone then let t be the time. rt = w; (x/2)t = 5x ==> t = 10.

what is wrong here, pls help. thanks.
Top
Post new topic Post Reply
• Page 1 of 1